Hilbert space split

Question

From the answer in Prove that, for a closed subspace $W$ of a vector space $V$, $(W^{\perp})^{\perp} = W$ we have that $W^- = (W^\perp)^\perp.$ How do we show that $V = W^- + W^\perp$?

I have proved this in the case of projections but finding it confusing to write down the solution completely in this case. Can some write down steps of hints?

Answer 1

For any closed subspace $M$ we have $V=M+M^{\perp}$. Take $M=W^{\perp}$. Note that $W^{\perp}$ is a closed subspace for any set $W$.